#857849 (C++17) No.2262 Fractions

提出ソース

結果

問題	No.2262 Fractions
ユーザー	👑 Nachia
提出日時	2023-04-08 11:18:11
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	54 ms / 2,000 ms
コード長	10,712 bytes
コンパイル時間	1,184 ms
コンパイル使用メモリ	97,924 KB
実行使用メモリ	7,964 KB
最終ジャッジ日時	2024-11-27 02:13:58
合計ジャッジ時間	3,362 ms
ジャッジサーバーID （参考情報）	judge1 / judge2

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	12 ms 6,400 KB
testcase_01	AC	54 ms 5,248 KB
testcase_02	AC	50 ms 5,248 KB
testcase_03	AC	47 ms 5,248 KB
testcase_04	AC	50 ms 5,248 KB
testcase_05	AC	42 ms 5,248 KB
testcase_06	AC	52 ms 5,248 KB
testcase_07	AC	51 ms 5,248 KB
testcase_08	AC	43 ms 5,248 KB
testcase_09	AC	49 ms 5,248 KB
testcase_10	AC	46 ms 5,248 KB
testcase_11	AC	28 ms 5,248 KB
testcase_12	AC	30 ms 5,248 KB
testcase_13	AC	29 ms 5,248 KB
testcase_14	AC	29 ms 5,248 KB
testcase_15	AC	28 ms 5,248 KB
testcase_16	AC	8 ms 5,248 KB
testcase_17	AC	8 ms 5,248 KB
testcase_18	AC	9 ms 5,248 KB
testcase_19	AC	20 ms 6,140 KB
testcase_20	AC	18 ms 5,940 KB
testcase_21	AC	18 ms 6,396 KB
testcase_22	AC	19 ms 6,012 KB
testcase_23	AC	18 ms 5,372 KB
testcase_24	AC	17 ms 7,964 KB
testcase_25	AC	18 ms 7,964 KB
testcase_26	AC	20 ms 7,704 KB
testcase_27	AC	21 ms 7,836 KB
testcase_28	AC	19 ms 7,708 KB
testcase_29	AC	19 ms 7,964 KB
testcase_30	AC	17 ms 7,836 KB
testcase_31	AC	19 ms 7,964 KB
testcase_32	AC	19 ms 7,964 KB
testcase_33	AC	21 ms 7,964 KB
testcase_34	AC	17 ms 7,964 KB
testcase_35	AC	13 ms 7,964 KB
testcase_36	AC	13 ms 7,840 KB
testcase_37	AC	7 ms 5,632 KB
testcase_38	AC	7 ms 5,504 KB
testcase_39	AC	15 ms 5,632 KB
testcase_40	AC	17 ms 5,632 KB
testcase_41	AC	19 ms 5,632 KB
testcase_42	AC	18 ms 5,628 KB
testcase_43	AC	14 ms 5,500 KB
testcase_44	AC	17 ms 7,960 KB
testcase_45	AC	19 ms 7,964 KB

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ソースコード

raw source code

#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\prime-sieve-explicit.hpp"

#include <vector>
#include <algorithm>
#include <cassert>
#include <iostream>


namespace nachia{

namespace prime_sieve_explicit_internal{
    std::vector<bool> isprime = { false }; // a[x] := isprime(2x+1)

    void CalcIsPrime(int z){
        if((int)isprime.size() *2+1 < z+1){
            int new_z = isprime.size();
            while(new_z*2+1 < z+1) new_z *= 2;
            z = new_z-1;
            isprime.resize(z+1, true);
            for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){
                for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false;
            }
        }
    }
    
    std::vector<int> prime_list = {2};
    int prime_list_max = 0;

    void CalcPrimeList(int z){
        while((int)prime_list.size() < z){
            if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

    void CalcPrimeListUntil(int z){
        if(prime_list_max < z){
            CalcIsPrime(z);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

}


bool IsprimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n == 2) return true;
    if(n % 2 == 0) return false;
    CalcIsPrime(n);
    return isprime[(n-1)/2];
}

int NthPrimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    CalcPrimeList(n);
    return prime_list[n];
}

int PrimeCountingExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n < 2) return 0;
    CalcPrimeListUntil(n);
    auto res = std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin();
    return (int)res;
}

// [l, r)
std::vector<bool> SegmentedSieveExplicit(long long l, long long r){
    assert(0 <= l); assert(l <= r);
    long long d = r - l;
    if(d == 0) return {};
    std::vector<bool> res(d, true);
    for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){
        long long il = (l+p-1)/p, ir = (r+p-1)/p;
        if(il <= p) il = p;
        for(long long i=il; i<ir; i++) res[i*p-l] = false;
    }
    if(l < 2) for(long long p=l; p<2 && p<r; p++) res[l-p] = false;
    return res;
}


} // namespace nachia
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

#line 8 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

namespace nachia{

template<class Elem>
void DivisorZeta(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i];
}

template<class Elem>
void DivisorInvZeta(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d];
}

template<class Elem>
void DivisorMobius(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i];
}

template<class Elem>
void DivisorInvMobius(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d];
}

template<class Elem>
std::vector<Elem> GcdConvolution(std::vector<Elem> a, std::vector<Elem> b){
    assert(a.size() == b.size());
    assert(1 <= a.size());
    DivisorInvZeta(a);
    DivisorInvZeta(b);
    for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
    DivisorInvMobius(a);
    return a;
}

template<class Elem>
std::vector<Elem> LcmConvolution(std::vector<Elem> a, std::vector<Elem> b){
    assert(a.size() == b.size());
    assert(1 <= a.size());
    DivisorZeta(a);
    DivisorZeta(b);
    for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
    DivisorMobius(a);
    return a;
}

}
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\floor-sum.hpp"

#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\floor-sum.hpp"
#include <utility>

namespace nachia{


// a : any value
// mod != 0
std::pair<long long, unsigned long long> SafeDiv(long long a, unsigned long long mod){
    using u64 = unsigned long long;
    if(a >= 0) return std::make_pair(0, (u64)a);
    if(mod >= (u64)1 << 62) return std::make_pair(-1, (u64)a + mod);
    long long q = a / mod;
    long long m = a % (long long)mod;
    if(m){ q--; m += mod; }
    return std::make_pair(q, m);
}

unsigned long long nC2Uint64(unsigned long long n){
    return (n%2) ? ((n-1)/2*n) : (n/2*(n-1));
}

// n : any
// 1 <= m
// a : any
// b : any
// n * a%m + b%m < 2**64
unsigned long long FloorSumU64Unsigned(
    unsigned long long n,
    unsigned long long m,
    unsigned long long a,
    unsigned long long b
){
    using u64 = unsigned long long;
    assert(1 <= m);
    u64 ans = 0;
    while(n){
        if(a >= m){
            ans += a / m * nC2Uint64(n);
            a %= m;
        }
        if(b >= m){
            ans += b / m * n;
            b %= m;
        }
        u64 y_max = a * n + b;
        if (y_max < m) return ans;
        n = y_max / m;
        b = y_max % m;
        y_max = a; a = m; m = y_max;
    }
    return ans;
}

// n : any
// 1 <= m
// a : any
// b : any
// (n+1) * m < 2**64
unsigned long long FloorSumU64Signed(
    unsigned long long n,
    unsigned long long m,
    long long a,
    long long b
){

    using u64 = unsigned long long;
    auto ua = SafeDiv(a, m);
    auto ub = SafeDiv(b, m);
    u64 ans = FloorSumU64Unsigned(n, m, ua.second, ub.second);
    ans += ua.first / m * nC2Uint64(n);
    ans += ub.first / m * n;
    return ans;
}

} // namespace nachia
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\rational-number-search.hpp"

namespace nachia{

class RationalNumberSearch{
public:
    RationalNumberSearch(unsigned long long maxVal){
        assert(maxVal < 1ull << 63);
        mx = maxVal;
    }
    bool hasNext(){ return state >= 0; }
    std::pair<unsigned long long, unsigned long long> getNext() const {
        switch(state){
        case 0: return { a0+a1, b0+b1 };
        case 1: return { a0+tr*a1, b0+tr*b1 };
        case 2: return { a1+tr*a0, b1+tr*b0 };
        case 3: return { a0+(tl+tr)/2*a1, b0+(tl+tr)/2*b1 };
        case 4: return { a1+(tl+tr)/2*a0, b1+(tl+tr)/2*b0 };
        }
        return {0,0};
    }
    void give(bool toRight){
        int x = toRight ? 1 : 0;
        switch(state){
        case 0:
            tl = 1; tr = 2;
            if(a0 + a1 > mx || b0 + b1 > mx){ state = -1; }
            else{ state = (toRight ? 1 : 2); }
            break;
        case 1: case 2:
            if(x ^ (2-state)){ state += 2; }
            else{ tr *= 2; tl *= 2; }
            break;
        case 3: case 4:
            ((x ^ (4-state)) ? tr : tl) = (tl+tr)/2;
            break;
        }
        while(givecheck());
    }
private:
    using UInt = unsigned long long;
    UInt a0=0, b0=1, a1=1, b1=0, tl=0, tr=0, mx;
    int state = 0;
    bool givecheck(){
        auto st = [this](int x){ state = x; return true; };
        auto trq = [this](UInt x0, UInt x1) -> bool {
            bool f = x0+tr*x1 > mx;
            if(f) tr = (mx-x0)/x1 + 1;
            return f;
        };
        bool f = false;
        switch(state){
        case -1 : break;
        case 0:
            if(a0 + a1 > mx || b0 + b1 > mx){ state = -1; }
            break;
        case 1:
            if(trq(a0,a1)) f = true;
            if(trq(b0,b1)) f = true;
            if(f) return st(3);
            break;
        case 2:
            if(trq(a1,a0)) f = true;
            if(trq(b1,b0)) f = true;
            if(f) return st(4);
            break;
        case 3:
            if(tl + 1 == tr){
                a0 += a1 * tl;
                b0 += b1 * tl;
                return st(0);
            }
            break;
        case 4:
            if(tl + 1 == tr){
                a1 += a0 * tl;
                b1 += b0 * tl;
                return st(0);
            }
            break;
        }
        return false;
    }
};

} // namespace nachia
#line 5 "..\\Main.cpp"
#include <string>
#line 8 "..\\Main.cpp"
#include <atcoder/modint>
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

using Modint = atcoder::static_modint<998244353>;

i64 countFracs(i64 N){
    vector<i64> cnt(N+1);
    for(i64 c=1; c<=N; c++) cnt[c] += c;
    nachia::DivisorMobius(cnt);
    i64 sumcnt = 0;
    for(int i=1; i<=N; i++) sumcnt += cnt[i];
    return sumcnt;
}

pair<i64,i64> testcase(){
    i64 N, K; cin >> N >> K;
    i64 cnt = countFracs(N);
    if(cnt * 2 - 1 < K) return {-1,-1};
    if(cnt == K) return {1,1};
    bool sw = false;
    if(cnt < K){ K = cnt*2 - K; sw = true; }

    vector<i64> quotients = {0};
    for(i64 k=1; k*k<N; k++) quotients.push_back(k);
    int qp1 = quotients.size();
    for(i64 k=1; k*k<=N; k++) quotients.push_back(N/k);
    reverse(quotients.begin() + qp1, quotients.end());
    int numQ = quotients.size()-1;

    vector<i64> mobius(N+1); mobius[1] = 1;
    nachia::DivisorMobius(mobius);
    vector<i64> mertens = mobius;
    rep(i,N) mertens[i+1] += mertens[i];

    auto srch = nachia::RationalNumberSearch(N);
    i64 a = 0, b = 0;
    i64 t = 0;
    while(srch.hasNext()){
        t++;
        i64 ax = srch.getNext().first;
        i64 bx = srch.getNext().second;
        i64 sumcnt = 0;
        rep(q,numQ){
            i64 times = mertens[quotients[q+1]] - mertens[quotients[q]];
            cnt = nachia::FloorSumU64Signed(quotients[numQ-q]+1, bx, ax, 0);
            sumcnt += times * cnt;
        }
        if(K <= sumcnt){ a = ax; b = bx; }
        srch.give(sumcnt < K);
    }

    if(sw) swap(a, b);
    return {a,b};
}

int main(){
    int T; cin >> T;
    rep(t,T){
        auto ans = testcase();
        if(ans.first < 0) cout << "-1\n"; else cout << ans.first << '/' << ans.second << '\n';
    }
    return 0;
}



struct ios_do_not_sync{
    ios_do_not_sync(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;

yukicoder

結果

テストケース

ソースコード